{
  "id": "1912.06732",
  "version": "v1",
  "published": "2019-12-13T22:48:36.000Z",
  "updated": "2019-12-13T22:48:36.000Z",
  "title": "On the approximation of rough functions with deep neural networks",
  "authors": [
    "Tim De Ryck",
    "Siddhartha Mishra",
    "Deep Ray"
  ],
  "comment": "30 pages",
  "categories": [
    "math.NA",
    "cs.LG",
    "cs.NA",
    "stat.ML"
  ],
  "abstract": "Deep neural networks and the ENO procedure are both efficient frameworks for approximating rough functions. We prove that at any order, the ENO interpolation procedure can be cast as a deep ReLU neural network. This surprising fact enables the transfer of several desirable properties of the ENO procedure to deep neural networks, including its high-order accuracy at approximating Lipschitz functions. Numerical tests for the resulting neural networks show excellent performance for approximating solutions of nonlinear conservation laws and at data compression.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-13T22:48:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "deep neural networks",
      "rough functions",
      "approximation",
      "eno procedure",
      "deep relu neural network"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}